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**Axioms of congruence**

K1 - Every line AB is congruent to itself and to the line BA.

K2 - If A, B are two different points and R is another point of the straight line g, then on each half straight line starting from R there is exactly one point - do my assignment for me , C or D, for which holds:

AB≅RC and AB≅RD respectively.

K3 - If a point A between points B and C lies on a straight line g and the point A' between points B' and C' lies on another straight line g', then with BA≅B'A' and AC≅A'C' BC≅B'C' also holds.

K4 - If A, B, C are three points not on a straight line and A', B' are two other points for which AB≅A'B' holds, then there is a point C' or C'' on each side of the straight line determined by A' and B' such that holds:

Δ ABC≅Δ A'B'C' and Δ ABC≅Δ A'B'C' respectively.

K5 - If A, B, C are three points not lying on a straight line and D is a point on the straight line determined by A, B, then it follows from

Δ ABC≅Δ A'B'C' and Δ ABD≅Δ A'B'D' also AD≅A'D'.

**Axiom of parallels - Euclidean axiom of parallels**

EP - For a straight line there is at most one straight line through a point not lying on it, which does not intersect the first straight line.

**Axiom of Continuity - Archimedes' Axiom**

S - By n-times subtracting the distance A0A1 on a straight line, one obtains the points An and An+1 with A0A1≅AnAn+1, where An lies between A0and An+1. If B is a point on the half-line going from A0 to A1 - homework help geometry , there is a natural number m such that B lies between A0and Am.

**Axioms of motion**

B1 - Every movement is a one-to-one mapping of space onto itself.

B2 - If the points A, B and C lie on a straight line - urgent essay writing service - and C lies between A and B, then the image points A', B' and C' also lie on a straight line and C' lies between A' and B'.

B3 - The successive execution of movements is again a movement.

B4 - For two figures there is at most one and only one movement that maps the first figure onto the second figure.

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